watches the people with basic math skills fight to the death over the answer
If you really wanna see a bloodbath, watch this:
You know that a couple has two children. You go to the couple's house and one of their children, a young boy, opens the door. What is the probability that the couple's other child is a girl?
Different compilers have robbed me of all trust in order-of-operations. If there's any possibility of ambiguity - it's going in parentheses. If something's fucky and I can't tell where, well, better parenthesize my equations, just in case.
There's quite a few calculators that get this wrong. In college, I found out that Casio calculators do things the right way, are affordable, and readily available. I stuck with it through the rest of my classes.
Casio does a wonderful job, and it's a shame they aren't more standard in American schooling. Texas Instruments costs more of the same jobs, and is mandatory for certain systems or tests. You need to pay like $40 for a calculator that hasn't changed much if at all from the 1990's.
Meanwhile I have a Casio fx-115ES Plus and it does everything that one did, plus some nice quality of life features, for less money.
TI did the same thing Quark and Adobe did later on – got dominance in their markets, killed off their competition, and then sat back and rested on their laurels thinking they were untouchable
EDIT: although in part, we should thank TI for one thing – if they hadn’t monopolized the calculator market, Commodore would’ve gone into calculators instead of computers
My Casio calculators get this wrong, even the newer ones. BTW the correct answer is 16, right?
(8 ÷ 2) × (2 + 2)8 ÷ (2 × (2 + 2))2 2 + 8 2 ÷ × .(× (÷ 8 2) (+ 2 2))Yes
8 / 2 (2+2)
8 / 2 (4)
4 (4)
16
No
8 / 2 (2+2)
8 / 2 (4)
8 / 8
1
No. Order of operations is left to right, not right to left. 1 is wrong.
In some countries we're taught to treat implicit multiplications as a block, as if it was surrounded by parenthesis. Not sure what exactly this convention is called, but afaic this shit was never ambiguous here. It is a convention thing, there is no right or wrong as the convention needs to be given first. It is like arguing the spelling of color vs colour.
This is exactly right. It's not a law of maths in the way that 1+1=2 is a law. It's a convention of notation.
The vast majority of the time, mathematicians use implicit multiplication (aka multiplication indicated by juxtaposition) at a higher priority than division. This makes sense when you consider something like 1/2x. It's an extremely common thing to want to write, and it would be a pain in the arse to have to write brackets there every single time. So 1/2x is universally interpreted as 1/(2x), and not (1/2)x, which would be x/2.
The same logic is what's used here when people arrive at an answer of 1.
If you were to survey a bunch of mathematicians—and I mean people doing academic research in maths, not primary school teachers—you would find the vast majority of them would get to 1. However, you would first have to give a way to do that survey such that they don't realise the reason they're being surveyed, because if they realise it's over a question like this they'll probably end up saying "it's deliberately ambiguous in an attempt to start arguments".
The real answer is that anyone who deals with math a lot would never write it this way, but use fractions instead
Please Excuse My Dear Aunt Sally, she downloaded a shitty ad-infested calculator from the Google Play store.
[...] the question is ambiguous. There is no right or wrong if there are different conflicting rules. The only ones who claim that there is one rule are the ones which are wrong!
https://people.math.harvard.edu/~knill/pedagogy/ambiguity/index.html
As youngsters, math students are drilled in a particular
convention for the "order of operations," which dictates the order thus:
parentheses, exponents, multiplication and division (to be treated
on equal footing, with ties broken by working from left to right), and
addition and subtraction (likewise of equal priority, with ties similarly
broken). Strict adherence to this elementary PEMDAS convention, I argued,
leads to only one answer: 16.Nonetheless, many readers (including my editor), equally adherent to what
they regarded as the standard order of operations, strenuously insisted
the right answer was 1. What was going on? After reading through the
many comments on the article, I realized most of these respondents were
using a different (and more sophisticated) convention than the elementary
PEMDAS convention I had described in the article.In this more sophisticated convention, which is often used in
algebra, implicit multiplication is given higher priority than explicit
multiplication or explicit division, in which those operations are written
explicitly with symbols like x * / or ÷. Under this more sophisticated
convention, the implicit multiplication in 2(2 + 2) is given higher
priority than the explicit division in 8÷2(2 + 2). In other words,
2(2+2) should be evaluated first. Doing so yields 8÷2(2 + 2) = 8÷8 = 1.
By the same rule, many commenters argued that the expression 8 ÷ 2(4)
was not synonymous with 8÷2x4, because the parentheses demanded immediate
resolution, thus giving 8÷8 = 1 again.This convention is very reasonable, and I agree that the answer is 1
if we adhere to it. But it is not universally adopted.
Everyone in this threading referencing PEMDAS and still thinking the answer is 1 are completely ignoring the part of the convention is left to right. Only way to get 1 is to violate left to right on multiplication and division.
The problem is that BIDMAS and its variants are lies-to-children. Real mathematicians don't use BIDMAS. Multiplication by juxtaposition is extremely common, and always takes priority over division.
Nobody in their right minds would saw 1/2x is the same as (1/2)x. It's 1/(2x).
That's how you get 1. By following conventions used by mathematicians at any level higher than primary school education.
I'm with the right answer here. / and * have same precedence and if you wanted to treat 2(2+2) as a single unit, you should have written it like (2*(2+2)).
It's pretty common even in academic literature to treat implied multiplication as having higher precedence than explicit multiplication/division. Otherwise an expression like 1 / 2n would have to be interpreted as (1 / 2) * n rather than the more natural 1 / (2 * n).
A lot of this bullshit can be avoided with better notation systems, but calculators tend to be limited in what you can write, so meh. Unless you want to mislead people for the memes, just put parentheses around things.
People keep debating over this stuff. I have a simpler solution. Math is not real.
this is why I never use ÷ (or more realistically "/") without explicit brackets denoting order of operations.
this comment section illustrates perfectly why i hate maths so much lmao
love ambiguous, confusing rules nobody can even agree on!
The problem isn't math, it's the people that suck at at it who write ambigous terms like this, and all the people in the comments who weren't educated properly on what conventions are.
lol, math is literally the only subject that has rules set in stone. This example is specifically made to cause confusion. Division has the same priority as multiplication. You go from left to right. problem here is the fact that you see divison in fraction form way more commonly. A fraction could be writen up as (x)/(y) not x/y (assuming x and y are multiple steps). Plain and simple.
The fact that some calculator get it wrong means that the calculator is wrongly configured. The fact that some people argue that you do () first and then do what's outside it means that said people are dumb.
They managed to get me once too, by everyone spreading missinformation so confidently. Don't even trust me, look up the facts for yourself. And realise that your comment is just as incorrect as everyone who said the answer is 1. (uhm well they don't agree on 0^0, but that's kind of a paradox)
Just write it out as a fraction and avoid all the confusion
The calculator is correct
People in this thread need to watch this: https://youtu.be/lLCDca6dYpA
The problem is that there's no "external" parentheses to really tell us which is right: (8 / 2) * 4 or 8 / (2 * 4)
The amount of comments here shows how much debate this "simple" thing generates
When there are no parentheses, you process left to right on the same tier of operations. That's how it's always been processed.
Afaik the order of operations doesn't have distributive property in it. It would instead simply become multiplication and would go left to right and would therefore be 16.
For anyone like me who has math as their worst subject: PEMDAS.
PEMDAS is an acronym used to mention the order of operations to be followed while solving expressions having multiple operations. PEMDAS stands for P- Parentheses, E- Exponents, M- Multiplication, D- Division, A- Addition, and S- Subtraction.
So we gotta do it in the proper order. And remember, if the number is written like 2(3) then its multiplication, as if it was written 2 x 3 or 2 * 3.
So we read 8/2(2+2) and need to do the following;
(2 + 2) and follow the order of operations within them, which gets us 4.2(4) which is the same as 2 x 4 which is 88 / 8 is 1.The answer is 1. The old calculator is correct, the phone app which has ads backed into it for a thing that all computers were invented to do is inaccurate.
Well that's just wrong... Multiplication and division have equal priorities so they are done from left to right. So: 8 / 2 * (2 + 2)=8 / 2 * 4=4 * 4=16
Uh.. no the 1 is wrong? Division and multiplication have the same precedence, so the correct order is to evaluate from left to right, resulting in 16.
The correct answer is 16. Multiplication and Division happen at the same level of priority, and are evaluated left-to-right.
No it's ambiguous, you claiming there is one right answer is actually wrong.
Left is correct; implicit multiplication takes precedence over explicit multiplication or division.
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